The present invention concerns an equalisation method and device for the downlink channel of a telecommunications system of the MC-CDMA type. More particularly, the present invention concerns an equalisation method and device of the GMMSE type.
Multi-Carrier Code Division Multiple Access (MC-CDMA) combines OFDM (Orthogonal Frequency Division Multiplex) modulation and the CDMA multiple access technique. This multiple access technique was proposed for the first time by N. Yee et al. in the article entitled “Multicarrier CDMA in indoor wireless radio networks” which appeared in Proceedings of PIMRC'93, Vol. 1, pages 109–113, 1993. The developments of this technique were reviewed by S. Hara et al. in the article entitled “Overview of Multicarrier CDMA” published in IEEE Communication Magazine, pages 126–133, December 1997.
Unlike the DS-CDMA (Direct Sequence Code Division Multiple Access) method, in which the signal of each user is multiplied in the time domain in order to spread its frequency spectrum, the signature here multiplies the signal in the frequency domain, each element of the signature multiplying the signal of a different subcarrier.
More precisely, FIG. 1 shows the structure of an MC-CDMA transmitter for a given user k. Let dk(t) be the ith symbol to be transmitted from the user k, where dk(i) belongs to the modulation alphabet. The symbol dk(i) is first of all multiplied at 110 by a spreading sequence or signature of the user, denoted ck(t), consisting of N “chips”, each “chip” being of duration Tc, the total duration of the spreading sequence corresponding to a symbol period T. The results of the multiplication of the symbol dk(i) by the different “chips” are converted by the serial to parallel converter 120 into a block of L symbols, where L is in general a multiple of N. It will be considered, for reasons of simplification of presentation, that L=N. The block of L symbols is then subjected to an inverse fast Fourier transformation (IFFT) in the module 130 before being transmitted to the parallel to serial converter 140. In order to prevent intersymbol interference, a guard interval, with a length greater than the duration of the pulse-type response of the transmission channel, is added to the MC-CDMA symbol. This interval is obtained by the addition (not shown) of a suffix chosen so as to be identical to the start of the said symbol. The symbol thus obtained is amplified at 150 in order to be transmitted over the user channel. It can therefore be seen that the MC-CDMA method can be analysed into a spreading in the spectral domain (before IFFT) followed by an OFDM modulation.
In practice, a base station transmits the data for a user k in the form of frames of I symbols, each symbol dk(i) being spread by a real signature ck(t) with a duration equal to the symbol period T, such that ck(t)=0 if t∉[0,T[. The signal modulated at time t=i.T+l.Tc can then be written, if the guard intervals between MC-CDMA symbols are omitted:
                                          S            k                    ⁡                      (            t            )                          =                              ∑                          i              =              0                                      I              -              1                                ⁢                                    ∑                              l                =                0                                            L                -                1                                      ⁢                                          v                k                            ·                                                c                  k                                ⁡                                  (                                      l                    .                                          T                      c                                                        )                                            ·                                                d                  k                                ⁡                                  (                  i                  )                                            ·                              exp                ⁡                                  (                                                            j                      ·                      2                                        ⁢                    π                    ⁢                                                                                  ⁢                                          l                      /                      L                                                        )                                                                                        (        1        )            where vk is the amplitude of the signal transmitted by the user k, assumed to be constant for a transmission unit.
An MC-CDMA receiver for a given user k has been illustrated schematically in FIG. 2.
The demodulated received signal is sampled at the “chip” frequency and the samples belonging to the guard interval are eliminated (elimination not shown). The signal obtained can be written:
                              R          ⁡                      (            t            )                          =                                            ∑                              k                =                0                                            K                -                1                                      ⁢                                          ∑                                  i                  =                  0                                                  I                  -                  1                                            ⁢                                                ∑                                      l                    =                    0                                                        L                    -                    1                                                  ⁢                                                                            h                      kl                                        ⁡                                          (                      i                      )                                                        ·                                      v                    k                                    ·                                      c                    kl                                    ·                                                            d                      k                                        ⁡                                          (                      i                      )                                                        ·                                      exp                    ⁡                                          (                                                                        j                          ·                          2                                                ⁢                        π                        ⁢                                                                                                  ⁢                                                  l                          /                          L                                                                    )                                                                                                    +                      b            ⁡                          (              t              )                                                          (        2        )            where K is the number of users, ckl=ck(l.Tc),hkl(i) represents the response of the channel of the user k to the frequency of the subearrier l of the MC-CDMA symbol transmitted at time i.T and where b(t) is the received noise.
If the downlink channel is considered, the transmission channels have identical characteristics and it is possible to write hkl=hl. The study will be limited hereinafter to the downlink channel.
The samples obtained by sampling at the “chip” frequency are put in parallel in a serial to parallel converter 210 before undergoing an FFT in the module 220. The samples in the frequency domain, output from 220, are equalised and despread by the signature of the user k. To do this, the samples of the frequency domain are multiplied by the coefficients ql.ckl* in the multipliers 2300, . . . , 230L−1, and then added at 240 in order to supply as an output an estimated symbol {circumflex over (d)}k(i).
Different possibilities of equalisation have been envisaged in the state of the art:                MRC (Maximumn Ratio Combining) defined by the use of the coefficients ql=ht* where .* denotes the complex conjugate;        EGC (Equal Gain Combining) defined by the use of the coefficients ql=e−jφl where hl=ρl.ejφl;        ZF (Zero Forcing) where ql=hl−1(i);        zero forcing ZF with threshold (Th) where ql=hl−1(i) if |hl(i)|<Th and ql=0 (or ql=e−jφl) otherwise;        the Minimum Mean Square Error (MMSE) algorithm for minimising the mean square error on each of the carriers:        
      q    l    =            h      l      *                                                      h            l                                    2            +              σ        2            where σ2 is the variance of the noise on the carrier.
In MC-CDMA, the presence of a guard period makes it possible to disregard the intersymbol interference. The equalisation can therefore be simply effected by means of a simple multiplication by a complex coefficient, carrier by carrier.
The receiver illustrated in FIG. 2 decodes the data of a user k without taking account of the interference due to the other users. For this reason it is known as single user or SU.
The multiuser detection techniques are known notably in CDMA telecommunications systems. They have the common characteristic of taking account of the interference generated by the other users.
A multiuser detection or MUD technique for MC-CDMA was presented in the article by J-Y. Beaudais, J. F. Hélard and J. Citeme entitled “A novel linear MMSE detection technique for MC-CDMA” published in Electronics Letters, Vol. 36, N°7, pages 665–666, 30 Mar. 2000. The equalisation method proposed no longer operates carrier by carrier but MC-CDMA symbol by MC-CDMA symbol, taking account of all the carriers. For this reason it is called GMMSE (Global Minimum Mean Square Error) equalisation or, equivalently, M-MMSE (Matrix Minimum Mean Square Error) equalisation. Its purpose is to minimise the mean square error between the estimated symbols {circumflex over (d)}k(i) and the transmitted symbols dk(i).
An MC-CDMA receiver with GMMSE equalization for a user k (also referred to in this case as per user MMSE) has been shown in FIG. 3. It differs from that of FIG. 2 in that the equalization is effected by means of a multiplication 331 by a matrix Q of the signals of the different carriers. The modules 310, 320 can be seen, identical to the modules 210 and 220 on FIG. 2. After the matrix multiplication 331, the samples are despread by the signature of user k. To do this, the samples of the frequency domain are multiplied by the coefficients ckl* in the multipliers 3320, . . . , 332L−1 and then added at 340. The despread signal obtained at the output of the adder 340 is then multiplied at 360 by the transmission level vk of the user κ in question in order to supply an estimated symbol {circumflex over (d)}k(i).
As shown in the aforementioned article, the matrix Q can be obtained by applying the Wiener filtering theory, in the form:Q=HH(AAH+σb2.IN)−1  (3)with A=HCV where H is the diagonal matrix N×N representing the frequency response of the channel to the different subearriers, C is the matrix N×N whose columns are the code sequences of the different users (which will hereinafter simply be referred to as “codes”), V is the diagonal matrix N×N whose elements vi are the transmission levels of the different users, σb2 is the variance of the noise and IN is the identity matrix of size N×N. The symbol .H designates the conjugate transpose. It should be noted that, in general, matrix inversion is not carried out but the corresponding system of linear equations is resolved.
As indicated by (3), the equalisation operation depends on the calculation of the matrix AAH and the inversion of the matrix AAH+σb2.IN (or equivalently the resolution of a linear system of rank N). These calculations consume resources of the mobile terminal, all the more so if they have to be performed frequently, notably in the case of rapid variations on the transmission channel. However, it is known that the resources of the terminals constitute precisely the critical part of a mobile telecommunication system.